Introduction. As well known (see, for example, [1]}, [2]}, [3]}), the weak turbulence theory is based on the assumption that the nonlinear interaction of waves is weak in comparison with the linear wave dispersion, which is determined by the dependence of the second derivative of the eigen frequency \(\omega \)  of small amplitude waves relative to the wave vector \(\mathbf {k}\) . As well known, for both deep water gravitational and capillary waves, the second derivative of \(\omega (\mathbf {k})\)  is nonzero in the entire range of wavenumbers. Thereby, initially Gaussian-distributed linear waves with different \(\mathbf {k}\)  almost remain this property when weak nonlinearity is taken into account. Each wave moving with its own frequency and wave vector experiences the influence of other waves at distances \(L\)  greater its wavelength, \(\propto k^{-1}\) . This makes it possible to describe the system of waves statistically in the random phase approximation using kinetic equations for the number of waves (quasiparticles) \(n_{k}\)  [1]}. In the leading approximation in nonlinearity, the kinetic equations describe either decay processes (\(1\rightarrow 2\) ), when
\(\omega _{k}=\omega _{k_{1}}+\omega _{k_{2}},\quad \mathbf {k}=\mathbf {k}_{1}+\mathbf {k}_{2}, \) 
